Canonical splittings of groups and 3-manifolds

We introduce the notion of a 'canonical' splitting over Z or Z x Z for a fi nitely generated group G. We show that when G happens to be the fundamental group of an orientable Haken manifold M with incompressible boundary, then the decomposition of the group naturally obtained from canonical splitting s is closely related to the one given by the standard JSJ-decomposition of M. This leads to a new proof of Johannson's Deformation Theorem.